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强聚焦高斯光束

光学捕获要求使用强聚焦的激光束。这样光束不能由常用近轴模型来描述。我们提出的表示不限于近轴情况下梁波方程解以下的家庭。在笛卡尔坐标x,y,z,设定可以表示为:

Equation

where jn are spherical Bessel functions of the first kind, k is the wavenumber, Pnm are associated Legendre functions, R = [x2 + y2 + (z - id)2]1/2, the parameter d corresponds to the Rayleigh range in the paraxial limit (i.e. d =  kw02/2, with beam waist radius w0) and   is the azimuth angle about the z axis. The above expression can be interpreted as a set of spherical harmonic waves centred on a complex point source-sink [Ulanowski & Ludlow 2000]. This set provides orthogonal solutions from which arbitrary beams can be constructed. The solution of order 01 corresponds in the paraxial limit to the familiar fundamental mode Gaussian beam, and in the far field it closely resembles the radiation pattern produced by a lens illuminated by a Gaussian beam. The field of the 01 order beam propagating along the z axis is shown in the graphic below for kd=2:

A higher order beam

较高阶光束(M = 3 N = 4)接下来所示,在纵向(XZ)和横向(XY)面:

animated gif
animated gif